Exact analytical analysis of via-coupling in multiple-layer structures

An efficient analysis of the capacitive via-plate coupling in multilayer printed-circuit board (PCB) structures is presented. The quasistatic solution for the via-plate capacitance is determined as the solution of Laplace´s equation for the static electric potential within the via-plate region, which is electrically small for a large frequency range. The final capacitance solution can be obtained by one single coefficient of the resulting linear equation system. The influence of additional via pads is readily included. An appropriate multiport equivalent circuit is set up by combination with the cavity impedances of the parallel-plane pairs. For frequencies where the whole structure is electrically small the model can be simplified to an equivalent circuit with coupled port inductances. The results are validated by 3D full-wave numerical simulations and measurements results.